Floquet dynamics in a one-dimensional chain in the multipulse spin locking of nuclear magnetic resonance

The dynamics of a one-dimensional chain that consists of $10$–$14$ dipolar-coupled nuclear spins, is placed in an external magnetic field, and is irradiated by a periodic sequence of resonant $\pi/n$ pulses ($n$ is a natural number) with the same time delay $2\tau$ between them has been studied. The numerical calculation has shown that thermodynamic equilibrium, which is determined by the common temperature of the Zeeman and dipole reservoirs, is established in the spin system at the average pulse field $\pi/(2n\tau)\sim\omega_{\text{loc}}$ (where $\omega_{\text{loc}}$ is the dipole frequency and $n>2$) and times $t\sim\omega_{\text{loc}}^{-1}$. The relaxation of the magnetization in the system irradiated by $(\pi/2)_x$ pulses at $\pi/{4\tau}\gg\omega_{\text{loc}}$ is due to a four-spin resonant process, and the relaxation rate is proportional to $\tau^4$.